Ajuda em trigonometria?

Comments

• pompeu

  June 2021

  sen(x) - sen (x/2) = 0

  2sen(x/2)(cos(x/2) - sen (x/2) = 0, põe sen(x/2) em evidência.

  sen(x/2)[2cos(x/2) - 1] = 0

  sen(x/2) = 0 => sen(x/2) = sen0 =>x/2 = 0 + kπ => x = 2kπ

  Obs. de π em π os valores se repetem.

  2cos(x/2) - 1 = 0 => 2cos(x/2) = 1 => cos(x/2) = 1/2 =>

  cos(x/2) = cos(π/3) => x/2 = π/3 + 2kπ => x = 2π/3 +4kπ

  cos(x/2) = cos(5π/3) =>x/2 = 5π/3 + 2kπ => x = 10π/3 +4kπ

  resposta

  1) x = 2kπ

  2) x = 2π/3 +4kπ

  3) x = 10π/3 +4kπ
• mmdc

  June 2021

  Formulinha

  sen(x) = sen(x/2 + x/2) = sen(x/2) cos(x/2) + cos(x/2) sen(x/2 )

  senx = 2sen(x/2)cos(x/2)